The uncertainties in the model of an energy distribution system made of a solar panel, a storage energy system and loads (power demanded by the end-users) are investigated, treating the epistemic variables as possibilistic and the aleatory ones as probabilistic. In particular, time-varying probabilistic distributions of the solar irradiation and the power demanded by the end-users is inferred from historical data. Then a computational framework for the joint propagation of both types of uncertainty is applied through the model of the energy distribution system to compute the Expected Energy Not Supplied.